A Concurrency from the Reflection of the Incircle's Contact Points across the Incenter
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Let ABC be a triangle. Let A', B', and C' be the intersections of the incircle with BC, CA, and AB, respectively. Let A'', B'', and C'' be the reflections of A', B', and C' across the incenter. Then AA'', BB'', and CC'' are concurrent.
Contributed by: Jay Warendorff (March 2011)
Open content licensed under CC BY-NC-SA
See problem 18 in Classical Theorems in Plane Geometry.